1. Field of Invention
The present invention relates to an image reconstruction technology, and more particularly to a projection method of 3D ray tracing applicable to image reconstruction.
2. Related Art
With the development of science and technology, a medical image becomes an effective diagnosis tool developed in modern times. The principle of a medical image involves establishing a mathematical model by using signals received by detectors during imaging and then reconstructing a 3D image by using an image reconstruction technology. To achieve a desirable image quality, technical improvements in hardware, the technology of establishing a reconstructed mathematical model, and the technology for finding a numerical solution, are all very important links. When a matrix model for describing the physical phenomenon of a system is more precise, the reconstructed image is more correct. A system matrix is subject to many factors such as penetration, detection efficiency, and spatial geometry. Therefore, the computation of a system matrix takes most of the time spent for the reconstruction. The focuses in the early development of the reconstruction technology are how to achieve effective storage and reduce computation. It becomes a trend in the development of the technology to introduce a precise model to the reconstruction technology. By comparison, conventional geometric modeling achieves low resolutions and will gradually fall short to meet the demands of practical applications in the future.
The description of image reconstruction can be represented by the following equation:[P]mxn[ fi]nx1=[ Cj]mx1,
where m denotes the total number of rays, that is, the number of ray responses that the system is capable to generate, for example, a LOR (line of response) in a positron emission tomography (PET) system, n denotes the total number of voxels, P denotes the model of the detection system, fi denotes an image to be reconstructed, and Cj denotes a detection result detected by a detection module.
The main component of Pmxn is a geometric distribution phenomenon, in which the basic definition of the matrix G of the spatial distribution is as follows:
            G              m        ×        n              =                  (                                                                                                                                                                                                                                                                                                                                                                g                ij                                                                                                                                                                                                                                                                                                                                                        )                    m        ×        n              ,
where gij represents a sensed geometric detection effect of the ith voxel with respect to the jth ray. Because a detector, at a different position, has a different probability to receive various rays, the information of gij needs to be fed back to the reconstruction process to correct the differences of spatial distribution, and is also referred to as a geometric factor.
Ray tracing is a conventional technology, and the specific optimized implementation solution of the process can be referred to the reference by Siddon R. L. (1985), which has gained wide use already. The ray tracing technology has significant influences and serves as the basis for the development of all types of image reconstruction technologies in the early period. Nowadays this technology is still used in physical calibration of crystal penetration or simulation of the trajectory a photon in space.
In ray tracing, according to the path of a detection ray in space, the length of the line segment passing through the voxel is taken as the geometric factor, or the length of a ray passing through the entire image space (field of view, FOV) is divided by the length of the ray passing through the image unit as an approximate value of the geometric factor. In this approach, a discrete-continuous problem occurs, when lines connecting the centers of detectors are used for approximation, the phenomenon that detectors cover an area fail to be described, and at the same time non-uniform model of source is fail to be described. When a voxel size is smaller than a detector, some voxels are evenly not passed through. To solve these problems, the number of detection rays needs to be increased, that is, to become sub-samples of detector. For example, the approach of Huesman R. H. (2000) is applicable to nuclear medicine imaging, in which a system model is introduced. Although a more accurate image result can be calculated, the computation cost grows geometrically. By taking this reference document as an example, when each detection unit is divided into 3×3 sub-detectors, because two group of detection units are divided by 9 times, and photons are received in pair, the total number of detection rays becomes 729 sub-rays as large. Although compression and simplification can be done by using the slope and ratio of detection rays, the effect is limited with respect to the price of O(n4). A ray tracing model is simple and has the advantages in computation, but to meet higher and higher requirements for the accuracy of imaging result, the technology needs to perform reconstruction processing on multiple detection sub-rays, the computation time is significantly increased, making it inapplicable in practice.
According to the accuracy demands in reconstruction, detection rays are divided into multiple detection sub-rays for computation, the computation cost becomes very high and makes it very difficult to apply the new-generation model-based image reconstruction technology in industry. Therefore, as for most commercially available imaging systems at present, to obtain an image result rapidly, a compromise is made with an image with a barely acceptable resolution, and a shift and add algorithm or conventional ray tracing is still used as the kernel for reconstruction.